Coordinate_Geometry

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Equation of Straight Line: 

Equation of Straight Line Equation of a straight line (gradient-intercept form) : y = m x + c where m is the gradient and c is the y-intercept . Equation of a straight line (given gradient and 1 point) :

Finding equations: 

Finding equations Find the equation of the straight line joining (2, 4) and (–2, 3) (–2, – 4) and (1, –7)

Finding equations: 

Finding equations Find the equation of the lines, given the gradient and the coordinate of a point lying on the line. (a) m = 3, (1, 1) (b) m = 0.5, (5, 7)

Finding Equations: 

Finding Equations What is the equation of the line which has gradient 2 and which passes through the origin?

Finding Equations: 

Finding Equations Find the equation of the straight line that is parallel to and bisects the line segment joining the points (3, 1) and (1, –5).

Finding Equations: 

Finding Equations Find the values of k if the line is parallel to

Finding Equations: 

Finding Equations Given the line, find its gradient; the coordinates of the point at which it cuts the x -axis.

Straight line equations of different forms: 

Straight line equations of different forms Double-intercept form General form Gradient-intercept form *Given gradient and 1 point

Collinear Points: 

Collinear Points 3 points are collinear if gradient AB = gradient BC

COORDINATE GEOMETRY: 

COORDINATE GEOMETRY Distance between 2 points Mid-point of 2 points

Distance between two points.: 

Distance between two points. 5 18 3 17 A(5,3) B(18,17) 18 – 5 = 13 units 17 – 3 = 14 units AB 2 = 13 2 + 14 2 Using Pythagoras’ Theorem, AB 2 = (18 - 5) 2 + (17 - 3) 2 y x

Distance between two points. In general,: 

Distance between two points. In general, x 1 x 2 y 1 y 2 A(x 1 ,y 1 ) B(x 2 ,y 2 ) Length = x 2 – x 1 Length = y 2 – y 1 AB 2 = (y 2 -y 1 ) 2 + (x 2 -x 1 ) 2 Hence, the formula for Length of AB or Distance between A and B is y x

Find the distance between the points (-1,3) and (2,-6): 

Find the distance between the points (-1,3) and (2,-6) Simply by using the formula: (-1,3) and (2,-6) (x 1 ,y 1 ) and (x 2 ,y 2 ) Since = 9.49 units (3 sig. fig)

The mid-point of two points.: 

The mid-point of two points. 5 18 3 17 A(5,3) B(18,17) Look at it’s horizontal length = 11.5 11.5 Look at it’s vertical length = 10 10 (11.5, 10) Mid-point of AB y x

The mid-point of two points.: 

The mid-point of two points. x 1 x 2 y 1 A(5,3) B(18,17) Look at it’s horizontal length Look at it’s vertical length Mid-point of AB y x y 2 Formula for mid-point is

Area: 

Area Area of a Polygon. Three points , and . The area of triangle ABC is given by This formula may be extended to a n sided polygon with n vertices. The area is then given by